capital budgeting problem
TRANSCRIPT
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Profitability Index (PI) or Benefit-Cost
Ratio (B/C Ratio)
The profitability index/present value index measures the present
value of returns per rupee invested. It is obtained dividing
the present value of future cash inflows (both operating
CFAT and terminal) by the present value ofcapital cash outflows.
The proposal will be worth accepting if the PI exceeds one.
Profitability IndexPresent value cash inflows
Present value of cash outflows=
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Example 8
When PI is greater than, equal to or less than 1, the net present value is
greater than, equal to or less than zero respectively. In other words, the
NPV will be positive when the PI is greater than 1; will be negative when the
PI is less than one. Thus, the NPV and PI approaches give the same results
regarding the investment proposals.
The selection of projects with the PI method can also be done on the basis
of ranking. The highest rank will be given to the project with the highest PI,
followed by others in the same order.
In Example 4 (Table 3) of machine A and B, the PI would be 1.22 for machine
A and 1.27 for machine B:
PI (Machine A) =Rs 69,645
= 1.24Rs 56,125
PI (Machine B) =Rs 71,521
= 1.27Rs 56,125
Since the PI for both the machines is greater than 1, both the machines are
acceptable.
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EVALUATION TECHNIQUES
(1) Traditional Techniques
(i) Average rate of return method
(ii) Pay back period method
(2) Discounted Cashflow (DCF)/Time-Adjusted (TA)
Techniques
(i) Net present value method
(ii) Internal rate of return method
(iii) Profitability index
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Average Rate of Return Method
The ARR is obtained dividing annual average profits after
taxes by average investments.
Average investment = 1/2 (Initial cost of machine ± Salvage
value) + Salvage value + net working
capital.
Annual average profits after taxes = Total expected after tax
profits/Number of years
The ARR is unsatisfactory method as it is based on
accounting profits and ignores time value of money.
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Example 4
Determine the average rate of return from the following data of twomachines, A and B.
Particulars Machine A Machine B
CostAnnual estimated incomeafter depreciation andincome tax:
Year 12345
Estimated life (years)Estimated salvage value
Rs 56,125
3,3755,3757,3759,375
11,37536,875
53,000
Rs 56,125
11,3759,3757,3755,3753,375
36,8755
3,000
Depreciation has been charged on straight line basis.
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Solution
ARR = (Average income/Average investment) × 100.
Average income of Machines A and B =(Rs 36,875/5) = Rs 7,375.
Average investment = Salvage value + 1/2 (Cost of machine ± Salvage
value) = Rs 3,000 + 1/2 (Rs 56,125 ± Rs 3,000) = Rs 29,562.50.
ARR (for machines A and B) = (Rs 7,375/Rs 29,562.50) × 100 = 24.9
per cent.
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Pay Back Method
The pay back method measures the number of years required for the CFAT
to pay back the initial capital investment outlay, ignoring interest
payment. It is determined as follows
(i) In the case of annuity CFAT: Initial investment/Annual CFAT.
(ii) In the case of mixed CFAT: It is obtained by cumulating CFAT till the
cumulative CFAT equal the initial investment.
Original/initial Investment (outlay) is the relevant cash outflow for a
proposed project at time zero (t = 0).
Annuity is a stream of equal cash inflows.
Mixed Stream is a series of cash inflows exhibiting any pattern other than
that of an annuity.
Although the pay back method is superior to the ARR method in that
it is based on cash flows, it also ignores time value of money
and disregards the total benefits associated with the investment proposal.
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Example 5
(i) In the case of annuity CFAT
An investment of Rs 40,000 in a machine is expected to
produce CFAT of Rs 8,000 for 10 years,
PB = Rs 40,000/Rs 8,000 = 5 years
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(ii) In the case of mixed CFAT
Table 2 presents the calculations of pay back period for Example 4.
Table 2
Year Annual CFAT Cumulative CFAT
A B A B
1
2
3
4
5
Rs 14,000
16,000
18,000
20,000
25,000*
Rs 22,00
0
20,000
18,000
16,000
17,000*
Rs 14,000
30,000
48,000
68,000
93,000
Rs 22,000
42,000
60,000
76,000
93,000
* CFAT in the fifth year includes Rs.3,000 salvage value also.
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Discounted Cashflow (DCF)/Time-Adjusted
(TA) Techniques
The DCF methods satisfy all the attributes of a good measure of
appraisal as they consider the total benefits (CFAT) as well as the
timing of benefits.
The present value or the discounted cash flow procedure
recognises that cash flow streams at different time periods differ in
value and can be compared only when they are expressed in terms
of a common denominator, that is, present values. It, thus, takes into
account the time value of money. In this method, all cash flows are
expressed in terms of their present values.
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The present value of the cash flows inExample 4 are illustrated in Table 3.
Table 3: Calculations of Present Value of CFAT.
Year Machine A Machine B
CFAT PV
factor
(0.10)
Present
value
CFAT PV
factor
(0.10)
Present
value
1 2 3 4 5 6 7
1
2
3
4
5
Rs 14,000
16,000
18,000
20,000
25,000*
0.909
0.826
0.751
0.683
0.621
Rs 12,726
13,216
13,518
14,660
15,525
69,645
Rs 22,000
20,000
18,000
16,000
17,000*
0.909
0.826
0.751
0.683
0.621
Rs 19,998
16,520
13,518
10,928
10,557
71,521
*includes salvage value.
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Net Present Value (NPV) Method
Net Present ValueCFt
(1+k)t=Sn + Wn
(1+k)n
COt
(1+k)t+ -
n
t=1
n
t=1
The NPV may be described as the summation of the present values of
(i) operating CFAT (CF) in each year and (ii) salvages value(S) and
working capital(W) in the terminal year(n) minus the summation
of present values of the cash outflows(CO) in each year. The present value
is computed using cost of capital (k) as a discount rate.
The decision rule for a project under NPV is to accept the project if the NPV
is positive and reject if it is negative. Symbolically,
(i) NPV > zero, accept, (ii) NPV < zero, reject
Zero NPV implies that the firm is indifferent to accepting or rejecting the
project.
The project will be accepted in case the NPV is positive.
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Example 6
In Example 4 we would accept the proposals of purchasing machines A and
B as their net present values are positive. The positive NPV of machine A is
Rs 13,520 (Rs 69,645 ± Rs 56,125) and that of B is Rs 15,396 (Rs 71,521 ± Rs
56,125).
In Example 4, if we incorporate cash outflows of Rs 25,000 at the end of the
third year in respect of overhauling of the machine, we shall find the
proposals to purchase either of the machines are unacceptable as their net
present values are negative. The negative NPV of machine A is Rs 6,255 (Rs
68,645 ± Rs 74,900) and of machine B is Rs 3,379 (Rs 71,521 ± Rs 74,900).
As a decision criterion, this method can also be used to make a choice
between mutually exclusive projects. On the basis of the NPV method, the
various proposals would be ranked in order of the net present values. The
project with the highest NPV would be assigned the first
rank, followed by others in the descending order. If, in our example, a
choice is to be made between machine A and machine B on the basis of the
NPV method, machine B having larger NPV (Rs 15,396) would be preferred
to machine A (NPV being Rs 12,520).
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Internal Rate of Return (IRR) Method
The IRR is defined as the discount rate (r) which equates the
aggregate present value of the operating CFTA received each year
and terminal cash flows (working capital recovery and salvage
value) with aggregate present value of cash outflows of an
investment proposal.
The project will be accepted when IRR exceeds the
required rate of return.
Internal Rate of
Return
CFt
(1+r)t=Sn + Wn
(1+r)n
COt
(1+r)t+ -
n
t=1
n
t=1
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The following steps are taken in determining IRR for an annuity.
Determine the pay back period of the proposed investment.
In Table A-4 (present value of an annuity) look for the pay back
period that is equal to or closest to the life of the project.
In the year row, find two PV values or discount factor (DFr) closest to
PB period but one bigger and other smaller than it.
From the top row of the table, note interest rate (r) corresponding to
these PV values (DFr).
IRR for an Annuity
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Determine actual IRR by interpolation. This can be done either directly using
Equation 1 or indirectly by finding present values of annuity (Equation 2).
IRR = r -PB ± DFr
(Equation 1)DFrL - DFrH
Where PB = Pay back period
DFr = Discount factor for interest rate r.
DFrL= Discount factor for lower interest rate
DFrH = Discount factor for higher interest rate.
r = Either of the two interest rates used in the formula
Alternatively, IRR = r -PVco ± PVCFAT
× ̈ r (Equation 2)¨PV
Where PVCO = Present value of cash outlay
PVCFAT = Present value of cash inflows (DFr x annuity)
r = Either of the two interest rates used in the formula
¨ r = Difference in interest rates
¨ PV = Difference in calculated present values of inflows
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Example 7
A project costs Rs 36,000 and is expected to generate cash inflows
of Rs 11,200 annually for 5 years. Calculate the IRR of the project.
Solution
(1) The pay back period is 3.214 (Rs 36,000/Rs 11,200)
(2) According to Table A-2, discount factors closest to 3.214 for 5
years are 3.274 (16 per cent rate of interest) and 3.199 (17 per cent
rate of interest). The actual value of IRR which lies between 16 per
cent and 17 per cent can, now, be determined usingEquations 1 and
2.
Substituting the values in Equation 1 we get: IRR = [(3.274-
3.214)/(3.274-3.199)] = 16.8 per cent.
Alternatively (starting with the higher rate), IRR = 17 ± [(3.214-
3.199)/(3.274-3.199)] = 16.8 per cent.
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Instead of using the direct method, we may find the actual IRR by applying
the interpolation formula to the present values of cash inflows and
outflows (Equation 2). Here, again, it is immaterial whether we start with
the lower or the higher rate.
PVCFAT (0.16) = Rs 11,200 × 3.274 = Rs 36,668.8
PVCFAT (0.17) = Rs 11,200 × 3.199 = Rs 35,828.8
IRR = 16 +36,668.8 ± 36,000
× 1 = 16.8 %36,668.8 ± 35,828.8
Alternatively (starting with the
higher rate), IRR = r -
(PVCO ± PVCFAT)× ¨ r
¨ PV
IRR = 17 -36,000 ± 35,828.8
× 1 = 16.8 %840
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Profitability Index (PI) or Benefit-Cost
Ratio (B/C Ratio)
The profitability index/present value index measures the present
value of returns per rupee invested. It is obtained dividing
the present value of future cash inflows (both operating
CFAT and terminal) by the present value ofcapital cash outflows.
The proposal will be worth accepting if the PI exceeds one.
Profitability IndexPresent value cash inflows
Present value of cash outflows=
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Example 8
When PI is greater than, equal to or less than 1, the net present value is
greater than, equal to or less than zero respectively. In other words, the
NPV will be positive when the PI is greater than 1; will be negative when the
PI is less than one. Thus, the NPV and PI approaches give the same results
regarding the investment proposals.
The selection of projects with the PI method can also be done on the basis
of ranking. The highest rank will be given to the project with the highest PI,
followed by others in the same order.
In Example 4 (Table 3) of machine A and B, the PI would be 1.22 for machine
A and 1.27 for machine B:
PI (Machine A) =Rs 69,645
= 1.24Rs 56,125
PI (Machine B) =Rs 71,521
= 1.27Rs 56,125
Since the PI for both the machines is greater than 1, both the machines are
acceptable.
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Assuming effective cost of capital of 8 per cent on World Bank loan to finance
the project and 35 per cent tax, present a financial analysis of the feasibility of
semi-automation of the Domanhill Colliery. As a financial consultant, what
recommendation would you make to the Board of Directors of Coal India Ltd?
Solution
Financial analysis for semi-mechanisation of Domanhill Colliery (using NPV
method)
Incremental cash outflows (Amount in crore of rupees)
Cost of new machine (SDL) (20 × Rs 1 crore)
Additional cost of semi-mechanisation
20
2
22
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Nature
Capital Budgeting is the process of evaluating and selecting
long-term investments that are consistent with the goal of
shareholders (owners) wealth maximisation.
Capital Expenditure is an outlay of funds that is expected to
produce benefits over a period of time exceeding one year.
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Such decisions are of paramount importance as they affect the
profitability of a firm, and are the major determinants of its efficiency
and competing power. While an opportune investment decision can
yield spectacular returns, an ill-advised/incorrect decision can
endanger the very survival of a firm.
Capital expenditure decisions are beset with a number of difficulties.
The two major difficulties are:
(1) The benefits from long-term investments are received in some
future period which is uncertain. Therefore, an element of risk is
involved in forecasting future sales revenues as well as the
associated costs of production and sales.
(2) It is not often possible to calculate in strict quantitative terms all
the benefits or the costs relating to a specific investment
decision.
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Capital budgeting decisions are of two
types
Such types of decisions are subject to less risk as the potential
cash saving can be estimated better from the past production
and cost data.
It is more difficult to estimate revenues and costs of a newproduct line.
(1) Investment Decisions Affecting Revenues
(2) Investment Decisions Reducing Costs
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Capital Budgeting Process
Capital Budgeting Process includes four distinct but interrelated steps used to evaluate
and select long-term proposals: proposal generation, evaluation, selection and follow
up.
Accept-reject Decision
Accept reject decision/approval is the evaluation of capital expenditure
proposal to determine whether they meet the minimum acceptance
criterion.
Mutually Exclusive Project Decisions
Mutually exclusive projects (decisions) are projects that compete with oneanother; the acceptance of one eliminates the others from further consideration.
Capital Rationing Decision
Capital rationing is the financial situation in which a firm has only fixedamount to allocate among competing capital expenditures.
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Cash Flows Vs. Accounting Profit
The capital outlays and revenue benefits associated with such
decisions are measured in terms of cash flows after taxes. The cash
flow approach for measuring benefits is theoretically superior to the
accounting profit approach as it
(i) Avoids the ambiguities of the accounting profits concept,
(ii) Measures the total benefits and
(iii) Takes into account the time value of money.
The major difference between the cash flow and the accounting profit
approaches relates to the treatment of depreciation. While the
accounting approach considers depreciation in cost computation, it
is recognised, on the contrary, as a source of cash to the extent of tax
advantagein the cash flow approach.
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Treatment of Depreciation
For taxation purposes, depreciation is charged (on the basis of written
down value method) on a block of assets and not on an individual asset. A
block of assets is a group of assets (say, of plant and machinery)
in respect of which the same rate of depreciation is prescribed by the
Income-Tax Act.
Depreciation is charged on the year-end balance of the block which is
equal to the opening balance plus purchases made during the year (in the
block considered) minus sale proceeds of the assets during the year.
In case the entire block of assets is sold during the year (the block ceases
to exist at year-end), no depreciation is charged at the year-end. If the sale
proceeds of the block sold is higher than the opening balance, the
difference represents short-term capital gain which is subject to tax.
Where the sale proceeds are less than the opening balance, the firm
is entitled to tax shield on short-term capital loss. The adjustment related
to the payment of taxes/tax shield is made in terminal cash inflows of the
project.